## PLUME INTERCEPTION BY A STREAM AND CONTAMINANT CONCENTRATIONS AT RECEPTOR WELLS LOCATED DOWNGRADIENT FROM THE STREAM

OFFICE OF RESOURCE CONSERVATION AND RECOVERY (ORCR) U.S. ENVIRONMENTAL PROTECTION AGENCY WAHSINGTON, D.C. 20460

FEBURARY, 20122 

## PLUME INTERCEPTION BY A STREAM AND CONTAMINANT CONCENTRATIONS AT RECEPTOR WELLS LOCATED DOWNGRADIENT FROM THE STREAM

1. INTRODUCTION

The U.S. Environmental Protection Agency’s Co mposite Model for Leachate Migration with Transformation Products (EPACMTP) was used to predict contaminant concentrations at receptor wells located downgradient of the co al combustion residues (CCRs) management sites (U.S. EPA, 2003a). The U.S. EPA has not made any changes to the source code of EPACMTP since its use for the Risk Assessment for th e CCRs (U.S. EPA, 2010). However, new pre-and post-processing modules were developed to a ddress the public and peer review comments regarding the interception of the plume by a surface-water body.

At some of the CCRs sites, a waste management unit (WMU) may be located in an area where the underlying aquifer is traversed by a surf ace-water body (a stream or a river, etc) downgradient from the WMU. At these sites, it is also possible that receptor wells may be located downgradient from the traversing surface-water bodies. In order to determine contaminant concentration at these wells, as we ll as contaminant mass fluxes that may enter the surface-water bodies from the aquifers, two proce dures have been developed. These procedures are described in Section 2 a nd are used to pre-process EP ACMTP input and post-process EPACMTP simulation results to take into consider ation the interception of a plume by a stream. The two procedures were developed for the case of gaining streams (streams receiving baseflow from groundwater) only. For losing streams (str eams discharging to groundwater), the streams receive no contaminants from groundwater and ther e is no added risk to receptors using the stream waters. In addition, in most hydrogeologic settings, the impact on the ground-water flow regime tends to be local and the regional groun dwater hydraulic gradient s are not significantly impacted by the presence of losing streams. Theoretical details of the two procedures are given in Section 2.



### 2. THEORETICAL FORMULATIONS

A waste management unit (WMU) is located upgradient from a surface-water body (e.g., a creek or a river) which traverses the region in the Y -direction and is normal to the regional groundwater flow direction which flows in the X -direction (Figure 1). The dist ance between the downgradient edge of the WMU and the upgradient edge of the surface-water body is X SW . A receptor well is located at a distance of X RW from the downgradient edge of the WMU. In the event that X RW > X SW , the well is located downgradient from the surface water body. Y B is a constant and represents the distance from the plume cen ter line to the pl ume width at the X = X RW where contaminant concentration in the plume is expected to be negligible. It represents the dimension of one half of the width of the flow and cont aminant transport domain along the Y-direction. Owing to the plume symmetry, only one half of the domain is simulated.3 Figure 1.  Plan view and definition of parameters.

As shown in Figure 2, the depth of the su rface water body below the water table is D SW , the depth of baseflow that discharg es to the surface-water body is D BF , and the saturated thickness of the aquifer is B

.

Figure 2.     Cross‐sectional view and definition of parameters

. If the surface-water body is a gaining stream, i. e., receiving baseflow flux from the aquifer, mathematical descriptions of groundwater fl ow and chemical transport in the aquifer downgradient from the surface-wat er body will have to be modi fied as the stream removes a portion of both water and chemical contaminants from the aquifer. In order to handle these special cases, two procedures were developed. The first pro cedure was developed to estimate chemical concentrations at a we ll downgradient from a traversi ng surface- water body, which, in turn, is downgradient from a WMU. The second procedure was developed to estimate chemical 

# z x Source Receptor Well

Flow Direction B D SW 

### Surface water body River, Creek

Aquifer base D BF Surface water body
River Creek Receptor well

Source Plume

X

‐ axis X SW YB

X RW4 mass flux removed by the traversing surface-wate r body. The two procedures are described in the following subsections.

2.1 Concentration at Wells Locate d Downgradient from a Stream

Within the flow domain shown in Figure 1, the total water flux removed by the gaining stream (henceforth a surface-water body is refe rred to as stream) is given by:

ܳ ஻௔௦௘௙௟௢௪ ൌ 2 ܻ ஻ ݍ ௔஻௦௘௙௟௢௪ ሺ1ሻ

Where: Q Baseflow = total baseflow water flux removed by the stream (L 3 /T);
q Baseflow = total baseflow water flux rem oved by the stream per unit width of the flow domain (L 2 /T); and Y

B = half widt h of the flow domain (L).

The aquifer also receives recharge from the inf iltration of precipitation within the flow domain (USEPA, 2003a). As a result, flow rate per unit width along the X

- direction may vary. To account for this variation, spatially averaged flow rate per unit wi dth is used. Average flow rate per unit width between the stream an d the receptor well is given by:

ݍ ஺௩௘௥௔௚௘ி௟௢௪ ൌ ଵ

௑ ೃೈ ି௑ ೄೈ ׬ ݍ ௥௘௙௜௨஺௤ ௫ୀ௑ ೃೈ ௫ୀ௑ ೄೈ ݀ݔ ሺ2ሻ

where:
q Averageflow = average aquifer flow rate per unit width of the flow domain with baseflow included (L 2 /T);
q

Aquifer = aquifer flow rate per unit width of the flow domain with baseflow included (L 2 /T); X

SW = distance to th e stream from the downgradient edge of the WMU (L); and X

RW = distance to the receptor well from the downgradient edge of the WMU (L).

After baseflow loss to the stream , the net aquifer flow rate per unit width (perpendicular to the stream) between the stream and the well is given by:

ݍ ே௘௧௙௟௢௪ ൌ ݍ ஺௩௘௥௔௚௘௙௟௢௪ െ ݍ ௔஻௦௘௙௟௢௪ ሺ3ሻ

where:
q Netflow = net aquifer flow rate per unit width of the flow domain with baseflow removed (L 2 /T).

The removal of groundwater as baseflow result s in changed groundwater flow rate per unit width, downgradient from the surface water body, from q Averageflow to q Netflow . It is, however, possible to use the same solution to the groundwat er flow and contaminan t transport equations based on q Averageflow by relocating the receptor well from X RW to X RW ’ , where X RW ’ represents an5 effective distance at which the concentration under the q Netflow condition between the stream and the receptor well is the same as that at X RW under the q Averageflow condition. The relocation procedure presented below is based on an assump tion that the dispersive flux is much smaller than the advective flux. This assumption holds when the Peclet number ([groundwater velocity* characteristic length]/longitudi nal dispersion coefficient or characteristic length/longitudinal dispersivity) is greater than 10 (Garges an d Baehr, 1998). An estimate based on the dispersitivity and receptor well distribution da ta in the EPACMTP Parameters/Data Background document (US EPA, 2003b), and using the receptor well distance as the ch aracteristic length, indicates that most of the s ites in EPACMTP have Peclet nu mbers varying from 10 to 5,000. Based on this assumption, a transformation procedure was developed. In the transformation, receptor well location is modifi ed using the equation below:

ሺ ܺ ᇱ ோௐ െ ܺ ௌௐ ሻ ൌ ௤ ಲೡ೐ೝೌ೒೐೑೗೚ೢ
௤ ಿ೐೟೑೗೚ೢ ሺ ܺ ோௐ െ ܺ ௌௐ ሻ ሺ4ሻ

Since q Netflow is not known a priori , it is necessary to locate X’ RW iteratively, as follows:

ܺ ത

ோௐ ൌ ଵ

ଶ ൫ܺ ோௐ ᇱ௜ ൅ ܺ ோௐ ᇱ௜ିଵ ൯ ሺ5ሻ

where: X ’i RW = i -th iterate of X’ RW with X ’0 RW = X RW

ݍԢ ே௘௧௙௟௢௪ ൌ ଵ

௑ ത ೃೈ ି௑ ೄೈ ׬ ݍ ௥௘௙௜௨஺௤ ௑ୀ௑ ത ೃೈ ௑ୀ௑ ೄೈ ݀ݔ  െ   ݍ ௔஻௦௘௙௟௢௪ ሺ6ሻ

Using X’ RW from Equation (5) to obtain average well location, ܺ ത

ோௐ , q Netflow is updated to q’ Netflow through Equation (6). Substituting q Netflow by q’ Neflow in Equation (4), X’ RW and therefore ܺ ത

ோௐ in Equation (5) are updated. The whole process is repeated until the difference between the most

current X’ RW is sufficiently close to the immediatel y preceding value. In other words, หܺ

ோௐ ᇱ௜ െ   ܺ ோௐ ᇱ௜ିଵ ห ൏ Є ሺ7ሻ

where: Є ൌ acceptable tolerance (a typical value is 0.1 meter)

.
This procedure is used to modify the existing well distance prior to EPACMTP simulations. By relocating the receptor well location to X’ RW from the downgradient edge of the WMU, concentration equivalent to concentr ation from the actual receptor well (located at the distance of X RW ) is calculated using the so lution of the groundwater flow and contaminant transport equations at the new well location, X’ RW . 2.2 Mass Flux from Aquifer into a Stream

To predict the mass flux of a contaminant from an aquifer to a stream, the distributions of contaminant concentration and volumetric groundw ater flux along the upgr adient edge of the stream must be known. The volumetric groundwate r flux depends on the difference between the6 stream stage and the hydraulic head in the aquifer. If the hydraulic head in the aquifer is higher than the stream stage, the groundw ater from the aquifer will enter the stream as baseflow. When this occurs, the stream is said to be a gaini ng stream. The procedure below was developed for the case of a gaining stream only.

The groundwater volumetric flux pe r unit area of stream bed is governed by the difference in groundwater hydraulic head, hydraulic conductivity of streambed, and streambed thickness. In many watersheds, baseflow in terms of volumetri c inflow rate per unit length of stream is available. Assuming that the ba se flow information is availabl e, mass flux may be estimated by integrating the product of baseflow flux per un it area and contaminant concentration over the total baseflow area. The total baseflow area is determined by the baseflow depth, D BF , and the domain half width, Y B . The total mass flux is determined us ing the baseflow rate and the output contaminant concentration from EPACMTP according to the equation below.

ܯ  ൌ   2 ௤ ಳೌೞ೐೑೗೚ೢ
஽ ಳಷ ׬ ׬ ܥ ሺ ܺൌܺ ௌௐ ݐ ,ݖ ,ݕ , ሻ ݖ ݀ݕ݀ ஽ୀ ௭ ಳಷ ௭ ୀ଴ ௬ୀ௒ ಳ ௬ୀ଴ (8)

where: D BF = baseflow depth (L) (see Figure 2 and Equation (9) below)

C

= chemical concentration at ܺൌܺ ௌௐ (M/L 3 );

x

= horizontal distance of stream from the downgradient edge of the WMU (L);

X

SW = distance of stream from the downgradient edge of the WMU (L);

y = horizontal distance from th e source centroid along the source plane (L, see U.S. EPA, 2003a); and z = vertical distance from th e source centroid along the source plane (L, see U.S. EPA, 2003a), positive downward.

The concentration term, C , is obtained from Equation ( 4.92) in the EPACMTP Technical Background Document (USEPA, 2003a) and ba seflow depth which is defined by:

ܦ ஻ி ൌ ௤ ಳೌೞ೐೑೗೚ೢ
௤ ಲ೜ೠ೔೑೐ೝ ܤ (9)

where: B = saturated thickness of the aquifer

The baseflow depth, D BF , which is based on the Dupuit approximation (Bear, 1972), is considered more accurate th an the surface water depth, D SW (Figure 2) for the following reasons: (1) baseflow is a measured quantity in gauged streams; (2) reference elevations for stream depth are not always known; (3) a reported stream depth for a given stream may not reflect its average depth; and (4) stream depth may not account for th e contraction of groundwater flow tube due to localized steepening of hydraulic gradie nt before entering the stream.7 

### 3. References

Bear, J. 1972. Dynamics of Fluids in Por ous Media. American Elsevier, New York.

Garges, J. A., and A. L. Baehr. 1998. Type Cu rves to Determine the Relative Importance of Advection and Dispersion of Solute Transport, Ground Water, 36(6):959-965.

U.S. EPA. 2003a. EPA’s Composite Model for Leachate Migration with Transformation Products (EPACMTP). Technical Backgr ound Document. Office of Solid Waste, Washington, DC, EPA53-R-03-002.

U.S. EPA. 2003b. EPA’s Composite Model fo r Leachate Migration with Transformation Products (EPACMTP). Parameters/Data B ackground Document. Offi ce of Solid Waste, Washington, DC, EPA53-R-03-003

U. S. EPA. 2010. Human and Ecological Risk A ssessment of Coal Com bustion Wastes. Office of Resource Conservation and Recovery, Washington, D.C. 20460.